The graphics cards that have been tested with the DH61HO are included in this list: Tested Peripherals for Intel Desktop Board DH61HO. If this card is not included in this list, it does not mean that it will not work; it just means that Intel did not verify that it would work (it may not have existed when the verification process was still ongoing).

Answering your last two questions is difficult; we are talking about a lower-end motherboard and likely a lower-end processor (though you do not say). Many of the features and performance improvements in today's cards are wasted when combined with lower-end boards and processors. As well, we are talking about a board that is four generations and five years out of date; there are many "modern" graphics cards that simply will not work with boards this old. For example, some newer cards have hardware expectations (for example, absolutely require PCIe 3.0 support) and/or firmware expectations (for example, BIOS that supports UEFI-only OpROMs) that older boards like this simply cannot meet.

Bottom line, all I can say is: try it and see. Try to find someplace that supports try-before-buy. I would also read some of the other postings related to this topic; there are cases where the firmware incompatibilities can be overcome and the board still used (in the O/S environment).